docs: def bend_rounded_Crane(Di, angle, rc=None, bend_diameters=None):
      r'''Calculates the loss coefficient for any rounded bend in a pipe
      according to the Crane TP 410M [1]_ method. This method effectively uses
      an interpolation from tabulated values in [1]_ for friction factor
      multipliers vs. curvature radius.
      
      .. figure:: fittings/bend_rounded.png
         :scale: 30 %
         :alt: rounded bend; after [1]_
  
      Parameters
      ----------
      Di : float
          Inside diameter of pipe, [m]
      angle : float
          Angle of bend, [degrees]
      rc : float, optional
          Radius of curvature of the entrance, optional [m]
      bend_diameters : float, optional (used if rc not provided)
          Number of diameters of pipe making up the bend radius [-]
  
      Returns
      -------
      K : float
          Loss coefficient [-]
  
      Notes
      -----
      The Crane method does match the trend of increased pressure drop as
      roughness increases.
  
      The points in [1]_ are extrapolated to other angles via a well-fitting
      Chebyshev approximation, whose accuracy can be seen in the below plot.
  
      .. plot:: plots/bend_rounded_Crane.py
      
      Examples
      --------
      >>> bend_rounded_Crane(Di=.4020, rc=.4*5, angle=30)
      0.09321910015613409
  
      References
      ----------
      .. [1] Crane Co. Flow of Fluids Through Valves, Fittings, and Pipe. Crane,
         2009.
      '''
      if not rc:
          if bend_diameters is None:
              bend_diameters = 5.0
          rc = Di*bend_diameters
      fd = ft_Crane(Di)
      
      radius_ratio = rc/Di
      if radius_ratio < 1.0:
          radius_ratio = 1.0
      elif radius_ratio > 20.0:
          radius_ratio = 20.0
      factor = horner(bend_rounded_Crane_coeffs, 0.105263157894736836*(radius_ratio - 10.5))
      K = fd*factor
      K = (angle/90.0 - 1.0)*(0.25*pi*fd*radius_ratio + 0.5*K) + K
      return K